Let uˉ=⟨0,−2⟩,vˉ=⟨4,3⟩, and wˉ=⟨0,-4⟩. Find the vector xˉ that satisfies 5uˉ−vˉ+xˉ=2xˉ+wˉ In this case, xˉ=

To find the vector x, we first need to rearrange the equation to isolate x on one side. The given equation is:

5u - v + x = 2x + w

Subtract x from both sides to get:

5u - v = x + w

Then, subtract w from both sides to isolate x:

x = 5u - v - w

Now, we can substitute the given vectors into the equation:

x = 5(0, -2) - (4, 3) - (0, -4)

Perform the operations:

x = (0, -10) - (4, 3) - (0, -4)

x = (-4, -13)

So, the vector x that satisfies the equation is x = (-4, -13).